〜がほしい

ほしい means "wanted", and it's an い-adjective, so it conjugates on its own: ほしくない (don't want), ほしかった (wanted). The thing wanted takes が: 新しいパソコンがほしいです, "I want a new computer".

ほしい is for things. To want to do something, use the たい form of the verb instead (next point): 行きたい, not 行くがほしい.

It describes the speaker's own wants. For someone else, Japanese reports it from outside: 弟は新しいゲームをほしがっています, "my brother wants a new game". And asking a superior 何がほしいですか is too direct; offer instead.